Random waves passing over a shallow bar are considered, in particular the amplification of bound harmonics in shoaling water, their subsequent release in deepening water, and the role of wave breaking. Calculations have been performed utilizing a set of coupled evolution equations for complex Fourier amplitudes based on ideal-fluid Boussinesq-type equations for the wave motion, supplemented with a quasi-linear dissipation term to account for wave breaking. This is used together with the assumption of random, independent initial phases to calculate the evolution of the energy spectrum of the random waves. The results show encouraging agreement with observed spectra both for nonbreaking waves and for breaking waves passing over a bar.